where \(U_{ik}\)  is the PMNS-matrix, \(i,k = \lbrace 1,2,3\rbrace \) , \(\alpha , \beta = \lbrace e,\mu ,\tau \rbrace \)  are flavours and \(h,h^{\prime } = \pm 1\)  are helicities.
Thus, the amplitudes \(\mathinner {\langle {\nu _i^{h^{\prime }}(0)|\nu _i^h(t)}\rangle }\)  are the quantities of interest for us. Using quite the same approach based on the eigendecomposition as was implemented in [1]}, the amplitudes can be computed as follows
\(\mathinner {\langle {\nu _i^{h^{\prime }}(t)|\nu _i^h(0)}\rangle } = \sum _s C_{is}^{h^{\prime }h} e^{-i E_i^s t},\) 
